Cut cauliflower into small florets.
Combine cauliflower florets in a medium saucepan with chicken broth, onion, garlic, and thyme.
Bring to a boil; reduce heat and simmer, partially covered, 10 minutes.
Remove from pan, reserving 1/3 of cauliflower.
Transfer remaining 2/3 to a food processor or blender OR use an immersion blender to blend until pureed. (*note: let cauliflower mixture cool slightly before using in a blender.)
In a large saucepan melt butter and flour over medium heat, stirring constantly.
Gradually mix in half & half; add salt and pepper.
Cook, stirring constantly, until mixture boils.
Blend in cauliflower puree and shredded cheese; heat, stirring occasionally, until cheese melts.
Stir in reserved cauliflower.
Garnish with fresh thyme or crispy fried onions, as desired.